Abstract. We propose a novel method for reasoning in the description logic SHIQ. After a satisfiability preserving transformation from SHIQ to the description logic ALCIb, the obtained ALCIb Tbox T is converted into an ordered binary decision diagram (OBDD) which represents a canonical model for T. This OBDD is turned into a disjunctive datalog program that can be used for Abox reasoning. The algorithm is worst-case optimal w.r.t. data complexity, and admits easy extensions with DL-safe rules and ground conjunctive queries.